Ramblemuse Touch Points

I recently had a massage teaching colleague ping me about: 1) Why we need mitochondria? and 2) How many molecules of ATP are used per second in typical muscle contractions? Both questions are a matter of energy, thus piquing my underlying physicist nature.

Glucose to ATP

The first question really was really along the lines of why, if adenosine diphosphate (ADP) and some extra phosphorous are available, they don’t just combine into adenosine triphosphate (ATP)? My answer was that the reaction is endothermic (energy absorbing). Think of it as being on a bike at the bottom of a hill. The bike isn’t just going to spontaneously move up the hill, you’re going to have to supply the energy to make it climb.

Being endothermic is one of two reasons that reactions often don’t “just happen”. The second reason is that a reaction, while exothermic (energy releasing), can have a substantial activation energy. This is, once again, like being on a bicycle, this time wanting to ride a couple of kilometers downhill to the beach. The problem is that, before the road starts downhill, it climbs to a place higher than where you are starting. So, you can’t just coast downhill, you have to put some energy in first to get over the hill in the middle before collecting on the downhill ride at the end. There’s a good short video from the Kahn Academy and also an even shorter animation.

As glycolysis breaks down glucose, it uses up two ATP early on and then churns out four ATP and two pyruvate in the end; a net gain of two ATP. Here’s a short animation and also material by Jon Maber covering glycolysis.

The mitochondria further convert ADP into ATP. They take the two pyruvate generated by glycolysis in the cytosol and oxidize it via the citric acid (Krebs) cycle to produce two further molecules of ATP, as shown in this short animation.

Most of the 36-38 ATP produced by breaking down glucose via both glycolysis and the Krebs cycle aren’t direct (i.e. substrate phosphorylation). They come via production of Nicotinamide adenine dinucleotide (NAD) as NADH and then the establishment of a proton gradient via the electron transport chain and transforming ADP to ATP via oxidative phosphorylation. When the net production of ATP energy is compared against the total possible energy from oxidation of glucose, it shows an efficiency of about 40%, the rest of the energy going into heat.

Note that pyruvate is the input fueling the Krebs Cycle. If glycolysis is occuring too rapidly for the aerobic Krebs cycle to process it, pyruvate will reversibly be converted into lactate. Clearly, lactate (aka lactic acid) isn’t a harmful waste product, but simply a means of temporarily storing partially processed fuel. Because it can be converted back into pyruvate, lactate is to glucose about what charcoal is to wood. Lactate may build up in the blood during anerobic exercise, but once that exercise is stopped, it’s concentration is halved every 15-25 minutes so that the lactate concentration rapidly returns to baseline, homeostatic levels (Plowman & Smith, Exercise Physiology for Health Fitness and Performance, 2007, p115).

So, the bottom line for production of ATP from glucose is that it is a multi-faceted, very energy intensive process. It takes a bit of “shoving” to get that third phosphate attached to yield the high-energy, unstable, molecule of ATP.

Using the ATP energy

While the nominal energy from breaking the bond of the third phosphate group in ATP is 30.5 kJ/mole, when the concentrations of ATP, ADP, phosphate, magnesium, and the pH are taken in to account, the effective free energy is approximately 50 kJ/mole, as discussed in terms of ATP hydrolysis and the free energy from such hydrolysis. Also the overall efficiency for producing mechanical energy from glucose in on the order of 20%, which, combined with the efficiency of 40% for producing ATP, means that the efficiency for converting ATP energy into mechanical work is about 50%.

There’s an estimate that working out on a rowing machine takes about 250 Watts of power (0.250 kJ/sec). I can also estimate the power required to lift my 750g ceramic cup full of coffee at a steady velocity of 2/3 m/sec against gravity (about 10 m/sec²). That comes to

P_cup = (0.750 kg) × (10 m/s²) × (2/3 m/s) = 5 Watts

For a known rate of mechanical power usage P, the rate of ATP breakdown (including a factor for 50% efficiency) is:

This is a rate of 2.4×10¹⁹ molecules of ATP per second per Watt of mechanical energy produced; 1.2×10²⁰ molec/sec to lift my coffee cup; and 6.0×10²¹ molec/sec to workout on the rowing machine. We need to continually make ATP because we use it up rapidly.